An object is subjected to a force in the north-east direction. To balance this force,a second force should be applied in the direction:

Read each statement below carefully and state with reasons,if it is true or false:
$(a)$ The magnitude of a vector is always a scalar.
$(b)$ Each component of a vector is always a scalar.
$(c)$ The total path length is always equal to the magnitude of the displacement vector of a particle.
$(d)$ The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time.
$(e)$ Three vectors not lying in a plane can never add up to give a null vector.

$0.4\hat i + 0.8\hat j + c\hat k$ represents a unit vector when $c$ is

Which of the following relations is correct?

If $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is ........ $^\circ$.

If a particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$,its displacement vector is: